The Netherlands international, 28, has been frozen out of the Inter team after refusing to agree a significant pay cut and his club have agreed a deal to sell him to the Turkish club immediately.
Galatasaray have revealed that their offer was of £6.2 million for the midfielder, which Inter accepted, but Sneijder continues to stall on the proposed deal.
"We'll wait another three or four days for Sneijder," said Galatasaray president Unal Aysal.
"If the deal collapses, we have alternatives. The figures quoted in the media are wrong. Our deal with Inter is worth €7.5million (£6.2m).
"The player knows our proposal. Inter are now calculating things with him. Our offer for his wages is below €5.5million. It is also true that our coach Fatih Terim wants Sneijder - he is the first name on the list."
He added: "I see no reason why the transfer should not go through. Even if it does collapse, it won't be the end of the world."
The veteran of the 2010 treble triumph has said that he needs more time as he decides whether a move to Turkey is the right decision for his career.
“The pressure being put on me is annoying,” the midfielder told the Gazzetta dello Sport. “Look, like all of the players who need to decide where to go this month, I have until January 31. I’m in no rush and I don’t want to be rushed.
“After all that has happened in the last few months, in the context that I along with my team-mates made football history here, I don’t want to hear pressure being put on me.
“My doubts do not have anything to do with the offers that I have received. It’s just that after all that I have done I don’t want to feel the way I do, almost forced to make an important life decision in a short space of time. It’s got nothing to do with money.”